ZusammenfassungDie Arbeit enthält Bemerkungen über den Intuitionismus and über seine Beziehungen zu anderen Gebieten der Grundlagenforschung. Innerhalb der intuitionistischen Mathematik werden, im Anschluss an die Kritik von Griss gegen den Gebrauch der Negation, Evidenzstufen unterschieden, abhängend von der Art, in der bedingte Konstruktionen zugelassen werden. Auch werden gewisse Schwierigkeiten in der Theorie der endlichen Spezies diskutiert. Was die Grundlagenforschung im Aligemeinen betrifft, wird bemerkt, dass sie die klassische Mathematik weitgehend in ihre intuitiven, formalen and platonischen Bestandteile zerlegt hat. Es wird (...) näher eingegangen auf die These von Church in der Theorie der rekursiven Funktionen.RésuméL'article contient des remarques sur l'intuitionisme et sur ses rapports avec les autres directions dans la recherche des fondements. Dans la mathématique intuitioniste, et en connexion avec la critique de Griss contre l'usage de la négation, on distingue des degrés d'évidence, dépendant de l'espèce de constructions conditionnées qui est admise. En outre, on discute certaines difficultés dans la théorie des espèces finies. Concernant la recherche des fondements en général, on remarque que les mathématiques classiques ont été scindées en leurs éléments intuitifs, formels et platonistes. Quelques remarques sur la thèse de Church dans la théorie des fonctions récursives terminent l'article.The paper contains remarks on intuitionism and its relations with other domains of foundational research. Inside the intuitionistic mathematics, in connection with Griss' criticism against the use of negation, different degrees of evidence are distinguished, depending upon the way in which conditioned constructions are admitted. Some difficulties in the theory of finite species are discussed. Concerning the foundational research in general it is observed that it has separated intuitive, formal and platonistic constituents in classical mathematics. Some remarks are made on Church's thesis in the theory of recursive functions. (shrink)

Attention is drawn to the fact that what is alternatively known as Dummett logic, Gödel logic, or Gödel-Dummett logic, was actually introduced by Skolem already in 1913. A related work of 1919 introduces implicative lattices, or Heyting algebras in today's terminology.

Recently discovered documents have shown how Gentzen had arrived at the final form of natural deduction, namely by trying out a great number of alternative formulations. What led him to natural deduction in the first place, other than the general idea of studying “mathematical inference as it appears in practice,” is not indicated anywhere in his publications or preserved manuscripts. It is suggested that formal work in axiomatic logic lies behind the birth of Gentzen’s natural deduction, rather than any single (...) decisive influence in the work of others. Various axiomatizations are explored in turn, from the classical axioms of Hilbert and Ackermann to the intuitionistic axiomatization of Heyting. (shrink)

In 1930, Johann von Neumann, together with Rudolf Carnap and Arend Heyting, participated in a conference held in Königsberg, called “Second Seminar on the Epistemology of Exact Sciences”. The idea behind the reunion of these three researchers was to compose a fairly faithful picture of the three main foundational programs of mathematics at the time: formalism, logicism, and intuitionism. The main objective of this paper is to propose an analysis of the text “The Formalist Foundation of Mathematics” presented by (...) von Neumann in this conference. We show how, from von Neumann's perspective, the problem of the consistency of mathematical theories results from the transformation of a genuinely philosophical question into a genuinely logical-mathematical question and how a proof of consistency could be seen as the solution to the foundational problem. In the final part of the text, we present some considerations about Gerhard Gentzen’s consistency proofs and their importance to contemporary proof theory. (shrink)

In the 1920s Heyting attempted at axiomatizing constructive geometry. Recently, von Plato used different concepts to axiomatize it. He used 14 axioms to formulate constructive apartness geometry, seven of which have occurrences of negation. In this paper we show with the help of ANDP, a theorem prover based on natural deduction, that four new axioms without negation, shorter and more intuitive, can replace seven of von Plato's 14 ones. Thus we obtained a near negation-free new system consisting of 11 (...) axioms. (shrink)

The reader of Juvenal's fifth satire, making his way through the new Oxford text edited by W. V. Clausen, finds the sweep of the poet's indignant rhetoric interrupted by the obeli of 104. Reference to Clausen's paper which he quotes in support of his proposed reading glaucis sparsus reveals that he proceeds from the assumption that the line is corrupt, and evidence that this is the case must be sought elsewhere.

Bibliography of A. A. Fraenkel (p. ix-x)--Axiomatic set theory. Zur Frage der Unendlichkeitsschemata in der axiomatischen Mengenlehre, von P. Bernays.--On some problems involving inaccessible cardinals, by P. Erdös and A. Tarski.--Comparing the axioms of local and universal choice, by A. Lévy.--Frankel's addition to the axioms of Zermelo, by R. Mantague.--More on the axiom of extensionality, by D. Scott.--The problem of predicativity, by J. R. Shoenfield.--Mathematical logic. Grundgedanken einer typenfreien Logik, von W. Ackermann.--On the use of Hilbert's [epsilon]-operator in scientific theories, (...) by R. Carnap.--Basic verifiability in the combinatory theory of restricted generality, by H. B. Curry.--Uniqueness ordinals in constructive number classes, by H. Putnam.--On the construction of models, by A. Robinson.--Interpretation of mathematical theories in the first order predicate calculus, by T. Skolem.--The elementary character of two notions from general algebra, by R. Vaught.--Foundations of arithmetic and analysis. Axiomatic method and intuitionism, by A. Heyting.--On rank-decreasing functions, by G. Kurepa.--On non-standard models for number theory, by E. Mendelson.--Concerning the problem of axiomatizability of the field of real numbers in the weak second order logic, by A. Mostowski.--Non-standard models and independence of the induction axiom, by M. O. Rabin.--Sur les ensembles raréfiés de nombres naturels, par W. Sierpinski.--Philosophy of logic and mathematics. Remarks on the paradoxes of logic and set theory, by E. W. Beth.--Logique formalisée et raisonnement juridique, par R. Feys.--Im Umkreis der sogenannten Raumprobleme, von H. Freudenthal.--Process and existence in mathematics, by H. Wang. (shrink)

Background: Only data of published study results are available to the scientific community for further use such as informing future research and synthesis of available evidence. If study results are reported selectively, reporting bias and distortion of summarised estimates of effect or harm of treatments can occur. The publication and citation of results of clinical research conducted in Germany was studied.Methods: The protocols of clinical research projects submitted to the research ethics committee of the University of Freiburg in 2000 were (...) analysed. Published full articles in several databases were searched and investigators contacted. Data on study and publication characteristics were extracted from protocols and corresponding publications.Results: 299 study protocols were included. The most frequent study design was randomised controlled trial , followed by uncontrolled studies , laboratory studies and non-randomised studies . 182 were multicentre studies including 97 international collaborations. 152 of 299 had commercial funding and 46 non-commercial funding. 109 of the 225 completed protocols corresponded to at least one full publication ; the publication rate was 48%. 168 of 210 identified publications were cited in articles indexed in the ISI Web of Science. The median was 11 citations per publication .Conclusions: Results of German clinical research projects conducted are largely underreported. Barriers to successful publication need to be identified and appropriate measures taken. Close monitoring of projects until publication and adequate support provided to investigators may help remedy the prevailing underreporting of research. (shrink)

In English, the present perfect, unlike future, past, and non-finite perfects, cannot be modified by so-called ‘positional’ adverbials (Comrie 1976, McCoard 1978, a.o.). This phenomenon is known as the present perfect puzzle (Klein 1992).

What does it mean for ethics to say, as Wittgenstein did, that philosophy “leaves everything as it is”? -/- Though clearly absorbed with ethical questions throughout his life and work, Wittgenstein's remarks about the subject do not easily lend themselves to summation or theorizing. Although many moral philosophers cite the influence or inspiration of Wittgenstein, there is little agreement about precisely what it means to do ethics in the light of Wittgenstein. -/- Ethics after Wittgenstein brings together an international cohort (...) of leading scholars in the field to address this problem. The chapters advance a conception of philosophical ethics characterized by an attention to detail, meaning and importance which itself makes ethical demands on its practitioners. Working in conversation with literature and film, engaging deeply with anthropology and critical theory, and addressing contemporary problems from racialized sexual violence against women to the Islamic State, these contributors reclaim Wittgenstein's legacy as an indispensable resource for contemporary ethics. (shrink)

'... this book represents a welcome addition to the literature on PP and is recommended for readers interested in risk assessment, decision making and the precautionary principle.' - Krishna Ravi Srinivas, Political Studies Review.

The meanings of temporal adverbials seem easy to describe, but the compositional interaction with tense and aspect is notoriously difficult to analyse because we (more accurately: I) do not understand yet the principles governing the tense/aspect architecture of natural languages well enough. One of the most difficult areas of temporal structure is the perfect, and the literature quoted in this article shows that there is little agreement on its meaning(s). I believe that we will make progress only by a careful (...) investigation of the meanings of temporal adverbials and by stating their formal semantics in a way which is precise enough to test empirical predictions. This is what the present article wants to do. It studies the interaction of the German durative temporal PP seit a ‘since a’ with tense, in particular with the perfect. (shrink)

The ethical problem in the present time.--The ethical principle.--A defence of the ethical principle.--Evolution of the ethical principle.--Morality and religion.--The present status of morality.

Consistent discriminatory practices associated with dark and black skin color underpin the persistence of colorism and racism in the Indian subcontinent. To understand better how skin color ideologies occupy the mind of people with the effect of marginalizing those with dark skin color and promoting whiteness as a social capital, we will apply the paradigm of situated affectivity. The conceptual tools developed in this framework will help to see how the environmental structures that perpetuate colorism have a pervasive influence on (...) individuals’ values and their emotional repertoire from a very young age. After having documented how the minds of individuals are invaded with discriminatory colorist positions, we will present how people indulge in processes of _user-resource_ interactions assumed to help regulating their affect, that in turn, result in re-enforcing again colorist and racist ideologies and practices. (shrink)

The current volume of the Parmenides Series "On Thinking" addresses our deepest and most personal experience of the world, the experience of "the present," from a modern perspective combining physics and philosophy. Many prominent researchers have contributed articles to the volume, in which they present models and express their opinions on and, in some cases, also their skepticism about the subject and how it may be (or may not be) addressed, as well as which aspects they consider most relevant in (...) this context. While Einstein might have once hoped that "the present" would find its place in the theory of general relativity, in a later discussion with Carnap he expressed his disappointment that he was never able to achieve this goal. This collection of articles provides a unique overview of different modern approaches, representing not only a valuable summary for experts, but also a nearly inexhaustible source of profound and novel ideas for those who are simply interested in this question. (shrink)

Artificial intelligence (AI) systems will increasingly be used to cause harm as they grow more capable. In fact, AI systems are already starting to help automate fraudulent activities, violate human rights, create harmful fake images, and identify dangerous toxins. To prevent some misuses of AI, we argue that targeted interventions on certain capabilities will be warranted. These restrictions may include controlling who can access certain types of AI models, what they can be used for, whether outputs are filtered or can (...) be traced back to their user, and the resources needed to develop them. We also contend that new restrictions on non-AI capabilities needed to cause harm will be required. For example, concerns about AI-enabled bioweapon acquisition have motivated efforts to introduce DNA synthesis screening. Though capability restrictions risk reducing use more than misuse (resulting in an unfavorable Misuse–Use Tradeoff), we argue that interventions on capabilities are warranted in some circumstances when other interventions are insufficient, the potential harm from misuse is high, and there are targeted interventions. We provide a taxonomy of interventions that can reduce AI misuse, focusing on the specific steps required for a misuse to cause harm (the Misuse Chain), and a framework to determine if an intervention is warranted. We exemplify our framework to three examples: predicting novel toxins, creating harmful images, and automating spear phishing campaigns. (shrink)